Determine the total possible number of orbitals and electrons for both 2s and 2p.
What is the maximum number of electrons per orbital? How are their spins related?
In this question i don't get how the spins are related?
In every orbital there CAN be two electrons (no more than two but they may have only one).
How are they related: They are the negative of each other; i.e., one has a spin of +1/2 and the other (if there is another) has a spin of -1/2.
Not to confuse you but most freshman texts only talk about the spin of +1/2 or -1/2 and they DON'T mention that this has been simplified because the units are h/2*pi. So the spin of one electron is 1/2*h/2*pi = h/4*pi and the other is -h/4*pi.
To determine the total possible number of orbitals and electrons for both 2s and 2p, we need to understand the way orbitals are organized in an atom.
The "2s" and "2p" notations refer to different types of orbitals found in the second energy level (n=2) of an atom. The "2s" orbital is a spherically symmetric orbital, while the "2p" orbitals are dumbbell-shaped orbitals oriented along different axes (x, y, and z).
The maximum number of electrons that can be accommodated in each orbital can be determined using the Pauli exclusion principle and the Aufbau principle. According to the Pauli exclusion principle, no two electrons within the same atom can have the same set of four quantum numbers (n, l, ml, and ms). The ms quantum number represents the spin of an electron, which can have two possible values: +1/2 or -1/2.
Therefore, each orbital can accommodate a maximum of two electrons, since there are two possible "spin states" for each orbital (upward spin or downward spin).
For the 2s orbital, there is only one orbital. Hence, it can accommodate a maximum of two electrons.
For the 2p orbital, there are three separate orbitals (2px, 2py, and 2pz), which can accommodate a maximum of six electrons (two electrons per orbitals).
So, the total possible number of orbitals for 2s is 1, and the total number of electrons is 2.
The total possible number of orbitals for 2p is 3, and the total number of electrons is 6.
Regarding the spins of the electrons, the two electrons in each orbital are said to have opposite spins. This means that if one electron has an upward spin (+1/2), the other electron in the same orbital will have a downward spin (-1/2), and vice versa. The opposite spins help prevent the electrons from repelling each other, allowing them to occupy the same orbital.